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Math Help - Interpolation of measured data

  1. #1
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    Interpolation of measured data

    I have a measured data set (x & y are inputs, z is the result at those measures):

    x y z
    0.036802 0.004908 0.07158
    0.036802 0.022135 0.10095
    0.130886 0.004908 0.09627
    0.130886 0.022135 0.12560

    I would like a formula for interpolation, to predict z for all input conditions x & y (within bounds), for example when x=0.0875 & y=0.0066.

    I have tried some some formulas, but nothing is predicting with much accuracy.

    Thanks for any help
    J
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  2. #2
    Grand Panjandrum
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    Interpolation of measured data

    Quote Originally Posted by jhasting
    I have a measured data set (x & y are inputs, z is the result at those measures):

    x y z
    0.036802 0.004908 0.07158
    0.036802 0.022135 0.10095
    0.130886 0.004908 0.09627
    0.130886 0.022135 0.12560

    I would like a formula for interpolation, to predict z for all input conditions x & y (within bounds), for example when x=0.0875 & y=0.0066.

    I have tried some some formulas, but nothing is predicting with much accuracy.

    Thanks for any help
    J
    As always with problems of this type it would be helpfull to
    know what process gives rise to the data, then we could fit
    it with to an appropriate function.

    However lacking such knowlege you could always try the
    4-point interpolator given in Abramowitz and Stegun:

    Suppose you know your functional value at points:

    (x_0,y_0),\ (x_0+h,y_0),\ (x_0,y_0+k),\ (x_0+h,y_0+k)

    then

    f(x_0+p.h,y_0+q.k)\ \approx \ (1-p).(1-q).f(x_0,y_0)\ +
    p.(1-q).f(x_0+h,y_0)\ +

    (1-p).q.f(x_0,y_0+k)\ +

    p.q.f(x_0+h,y_0+k)
    Preferably with 0 \leq p \leq 1 and 0 \leq q \leq 1 .
    Last edited by CaptainBlack; November 11th 2005 at 12:13 AM. Reason: error in text
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  3. #3
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    Thanks, I don;t think your formula will work in this case. This data is measured data, it does not have a fucntion. The application is for CMOS ASIC circuit design static timing. Libraries are modeled at certain operating conditions and specified in tables. THe x axis data I provided would be the input transition of the wire to a logic gate pin, the y asix data I provided would be the output capatance of the wire to the logic gate output pin. Since fast results are required, interpolaion of the data is used. So for a logic cell modeled in a library, if you know the input transition and the output capactance, you should be able to interpolate the delay. The only requirement on the data should be that the input transition (x axis data) is within it's bounds, and hte same with the output capactance y data. I cannot use equations with more restrictions.

    Thanks for any help, and any time you've already spent.
    J
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by jhasting
    Thanks, I don;t think your formula will work in this case. This data is measured data, it does not have a fucntion. The application is for CMOS ASIC circuit design static timing. Libraries are modeled at certain operating conditions and specified in tables. THe x axis data I provided would be the input transition of the wire to a logic gate pin, the y asix data I provided would be the output capatance of the wire to the logic gate output pin. Since fast results are required, interpolaion of the data is used. So for a logic cell modeled in a library, if you know the input transition and the output capactance, you should be able to interpolate the delay. The only requirement on the data should be that the input transition (x axis data) is within it's bounds, and hte same with the output capactance y data. I cannot use equations with more restrictions.

    Thanks for any help, and any time you've already spent.
    J
    Just use you measured values for the f values in the formula,
    it will do the interpolation for you

    RonL
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  5. #5
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    The tables do not have all values for trans & cap, they are usually 7x7, so you need to interpolate.
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by jhasting
    The tables do not have all values for trans & cap, they are usually 7x7, so you need to interpolate.
    I give up. What I have quoted is an interpolation formula
    which allows you to interpolate into data tabulated on a
    regular grid.

    RonL
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